procedure

Melt 2 tablespoons butter with 2 tablespoons olive oil in heavy large pot over medium heat. Add sliced fennel and onions. Cover and cook until fennel is tender, stirring occasionally, about 15 minutes. Add potatoes and chicken stock; increase heat and bring to boil. Reduce heat, cover and simmer until potatoes are very tender, about 30 minutes. Remove from heat. Mix in Pernod. Season to taste with salt and pepper.

Working in batches, purée soup in blender. Transfer soup to large bowl. Mix in 2 cups half and half. Season soup to taste with salt and pepper. Cool slightly. Chill soup uncovered until cold, then cover and refrigerate.